Cetaceans (whales, dolphins and porpoises) have evolved flippers that aid in effective locomotion through their aquatic environments. Differing evolutionary pressures upon cetaceans, including hunting and feeding requirements, and other factors such as animal mass and size have resulted in flippers that are unique among each species. Cetacean flippers may be viewed as being analogous to modern engineered hydrofoils, which have hydrodynamic properties such as lift coefficient, drag coefficient and associated efficiency. Field observations and the collection of biological samples have resulted in flipper geometry being known for most cetacean species. However, the hydrodynamic properties of cetacean flippers have not been rigorously examined and thus their performance properties are unknown. By conducting water tunnel testing using scale models of cetacean flippers derived via computed tomography (CT) scans, as well as computational fluid dynamic (CFD) simulations, we present a baseline work to describe the hydrodynamic properties of several cetacean flippers. We found that flippers of similar planform shape had similar hydrodynamic performance properties. Furthermore, one group of flippers of planform shape similar to modern swept wings was found to have lift coefficients that increased with angle of attack nonlinearly, which was caused by the onset of vortex-dominated lift. Drag coefficient versus angle of attack curves were found to be less dependent on planform shape. Our work represents a step towards the understanding of the association between performance, ecology, morphology and fluid mechanics based on the three-dimensional geometry of cetacean flippers.